TY - JOUR
T1 - Maximization of quadratic forms expressed by distance matrices
AU - Izumino, Saichi
AU - Nakamura, Noboru
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - If x, y, z are real numbers satisfying x + y + z = 1, then the maximum of the quadratic form axy + bxz + cyz with positive constants a, b, c is abc/2ab + 2ac + 2bc − a2 − b2 − c2 under the assumption √a < √b + √c. Extending this fact, we give the maximum of the quadratic form ∑1≤iijxixj in n-variables x1, …, xn satisfying ∑ni=1 xi = 1 with constants aij = 0 under certain assumptions.
AB - If x, y, z are real numbers satisfying x + y + z = 1, then the maximum of the quadratic form axy + bxz + cyz with positive constants a, b, c is abc/2ab + 2ac + 2bc − a2 − b2 − c2 under the assumption √a < √b + √c. Extending this fact, we give the maximum of the quadratic form ∑1≤iijxixj in n-variables x1, …, xn satisfying ∑ni=1 xi = 1 with constants aij = 0 under certain assumptions.
KW - Distance matrix
KW - Ozeki’s inequality
KW - Quadratic form
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U2 - 10.14492/hokmj/1285766422
DO - 10.14492/hokmj/1285766422
M3 - Article
AN - SCOPUS:85035292234
VL - 35
SP - 641
EP - 658
JO - Hokkaido Mathematical Journal
JF - Hokkaido Mathematical Journal
SN - 0385-4035
IS - 3
ER -